Question

A and b are vectors that are not parallel.

FG = 2a − 3b
-
Choose all of the vectors below which are parallel to
FG.
a-b10a-15
3a-2b-4a+6b 2a + 3b
2a-3b-4a 2a-12b +4a + 3b

Answer 1

`\boxed{\textbf{a}-(3)/(2)\textbf{b}}`

`\boxed{10 \textbf{a}-15\textbf{b}}`

`\boxed{-4 \textbf{a}+6\textbf{b}}`

`\boxed{2\textbf{a}-12\textbf{b}+4\textbf{a}+3\textbf{b}}`

Explanation:

Given vector:

`\overrightarrow{\rm FG}=2 \textbf{a}-3\textbf{b}`

Two vectors are parallel if one can be written as a scalar multiple of the other.

Therefore, the following vectors are parallel to FG:

`\textbf{a}-(3)/(2)\textbf{b}=(1)/(2)(2 \textbf{a}-3\textbf{b})`

`10 \textbf{a}-15\textbf{b}=5(2 \textbf{a}-3\textbf{b})`

`-4 \textbf{a}+6\textbf{b}=-2(2 \textbf{a}-3\textbf{b})`

`2\textbf{a}-12\textbf{b}+4\textbf{a}+3\textbf{b}=6\textbf{a}-9\textbf{b}=3(2 \textbf{a}-3\textbf{b})`